Optical Topography with Compressive Sampling

Optical Topography is a fast non-invasive method for imaging function in the brain using light in the visible and near -infra red region. It uses a distribution of sources and detectors on the surface of the head, with a relatively small number of data, and a reconstruction into potentially 1000's of voxels. Thus
the reconstruction problem is severely under-determined, and regularisation methods are required

Figure 1a: Sagittal slices across 3D imageof absorption change
in infant brain due to passive movement of left arm.

Figure 1b: Sagittal slices across 3D image of absorption change
in infant brain due to passive movement of right arm.

Up to now, conventional regularisation techniques produce rather low resolution and blurred images. A new topic in the inverse problem community is Compressive Sampling (see for example
Compressive Sampling Resources). These methods seek to find a distribution of signals that give the sparsest image that is consistent with the data. They have shown dramatic performance in related fields such as MRI, and Geophysics

In this project we will apply these methods to the optical tomography problem. The optical modelling will use the UCL TOAST software which allows fast large scale modelling in Matlab.This will be combined with some of the existing
compressive sampling software). The project will suit someone interested in numerical methods, signal processing and medical imaging.